Answer:
The perimeter of the equilateral triangle, P = 24 units
Step-by-step explanation:
All sides of an equilateral triangle are equal. The height of the equilateral triangle is given by :
[tex]h=\dfrac{\sqrt{3} }{2}\times a[/tex]
a is the side of triangle
If the height of an equilateral triangle is, [tex]h=4\sqrt{3}[/tex]
Equation (1) becomes,
[tex]a=\dfrac{2h}{\sqrt{3} }[/tex]
Put h in above formula. So,
[tex]a=\dfrac{2\times 4\sqrt{3}}{\sqrt{3} }[/tex]
a = 8
So, the side of triangle is 8. The sum of all sides is called perimeter of any figure. So,
[tex]P=8\times 3[/tex]
P = 24 units
So, the perimeter of the equilateral triangle is 24 units. Hence, this is the required solution.
Final answer:
To find the perimeter of the equilateral triangle with a height of 4√3, we determine the side length using the relationship between the height and side length of the triangle, and then multiply by three to get a perimeter of 24 units.
Explanation:
The height of an equilateral triangle is given as 4√3. To find the perimeter, we need to determine the length of a side of the triangle. In an equilateral triangle, the height (h) creates a right-angled triangle where the height is opposite to a 60° angle, and the half of a side of the triangle (half-base) is adjacent to it. The relationship is given by the equation h = (a√3)/2, where a is the side length of the equilateral triangle. By substituting the height with 4√3, we get:
4√3 = (a√3)/2 → a = 8
Since all sides of an equilateral triangle are equal, the perimeter is three times the side length, which means the perimeter P = 3 × 8 = 24 units.
Mr. Lee asks a student to solve the following system of linear equations. {-28=-40q-14p 10q+4=2p Which ordered pair (p, q) is a solution to the system? (-7/5,-2) (-2,-7/5) (0, 2) (2, 0)
Answer:
p = 2 , q = 0
Step-by-step explanation:
Solve the following system:
{-28 = -14 p - 40 q | (equation 1)
10 q + 4 = 2 p | (equation 2)
Express the system in standard form:
{14 p + 40 q = 28 | (equation 1)
-(2 p) + 10 q = -4 | (equation 2)
Add 1/7 × (equation 1) to equation 2:
{14 p + 40 q = 28 | (equation 1)
0 p+(110 q)/7 = 0 | (equation 2)
Divide equation 1 by 2:
{7 p + 20 q = 14 | (equation 1)
0 p+(110 q)/7 = 0 | (equation 2)
Multiply equation 2 by 7/110:
{7 p + 20 q = 14 | (equation 1)
0 p+q = 0 | (equation 2)
Subtract 20 × (equation 2) from equation 1:
{7 p+0 q = 14 | (equation 1)
0 p+q = 0 | (equation 2)
Divide equation 1 by 7:
{p+0 q = 2 | (equation 1)
0 p+q = 0 | (equation 2)
Collect results:
Answer: {p = 2 , q = 0
Answer:
p = 2 , q = 0
Step-by-step explanation:
Trust me
Margaret has a bag containing 6 red
chips and 6 blue chips. What is the
probability of drawing two red chips in two
draws without replacement?
Answer:It will be 2/12
Step-by-step explanation:
6 blue chips 6 red chips
6+6=12 so 2 red chips to 12 =2/12
Can someone please help me with this question.
sorry for the quality but you have to find the surface area of this figure. pllleeeaasssee help
Answer:
S.A. = 36 cm²Step-by-step explanation:
First step:
Calculate the hypotenuse of a right triangle.
Use the Pythagorean theorem:
[tex]h^2=3^2+4^2\\\\h^2=9+16\\\\h^2=25\to h=\sqrt{25}\\\\h=5\ cm[/tex]
Second step:
We have
two right triangles with legs a = 3cm and b = 4 cm
one rectangle 4cm × 2cm
one rectangle 3cm × 2cm
one rectangle 5cm × 2cm
Calculate each area:
The formula of an area of a right triangle:
[tex]A=\dfrac{ab}{2}[/tex]
Substitute:
[tex]A_1=\dfrac{(3)(4)}{2}=(3)(2)=6\ cm^2[/tex]
The formula of an area of a rectangle l × w:
[tex]A=lw[/tex]
Substitute:
[tex]A_2=(4)(2)=8\ cm^2\\\\A_3=(3)(2)=6\ cm^2\\\\A_4=(5)(2)=10\ cm^2[/tex]
Third step:
Calculate the Surface Area of the figure:
[tex]S.A.=2A_1+A_2+A_3+A_4[/tex]
Substitute:
[tex]S.A.=2(6)+8+6+10=36\ cm^2[/tex]
^^^^^^^^^^^^^^^^^^^^
Answer:
Option B.
Step-by-step explanation:
The constant of proportionality is the constant value of the ratio of two proportional quantities x and y; usually written y = kx, where k is the factor of proportionality.
Given that the graph is a straight line, we can find the constant of proporctionality just by selecting a point, and then dividing the y-value by the x-value.
We can see from the graph that when y=5, x=4. Then, the constant of proportionality comes to be:
k = 5/4 = 1.25.
Then, the correct option is Option B.
subtract and simplify
Answer:
D
Step-by-step explanation:
Since the denominators of both fractions are common, then subtract the numerators leaving the common denominator, that is
[tex]\frac{4a+1-2a-7}{a^2-4}[/tex] = [tex]\frac{2a-6}{a^2-4}[/tex]
Answer:
[tex]\boxed{\bold{\frac{2a-6}{a^2-4}}}[/tex]
Explanation:
Apply Rule [tex]\bold{\frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}}[/tex]
= [tex]\bold{\frac{4a+1-\left(2a+7\right)}{a^2-4}}[/tex]
Expand [tex]\bold{4a+1-\left(2a+7\right): \ 2a-6}[/tex]
= [tex]\bold{\frac{2a-6}{a^2-4}}[/tex]
Mordancy.
Choose the point-slope form of the equation below that represents the line that passes through the points (-6, 4) and (2.0).
y-4 =-1/2(x+6)
y - 4 = 2(x + 6)
y+6=-1/2(x-4)
y+ 6 = 2(x-4)
Answer:
y - 4 = -1/2(x+6).
Step-by-step explanation:
The equation of the line is: y - y0 = m(x-x0)
If the line passes through the points (x1, y1)=(-6, 4) and (x1, y1)=(2, 0). Then, the slope is:
[tex]m = \frac{y1-y0}{x1-x0} = \frac{0-4}{2-(-6)} = -\frac{1}{2} [/tex]
Then, the equation is: y - 4 = -1/2(x+6).
Which of the following is a description of the data with a correlation coefficient of 0.8?
no correlation
perfect positive correlation
high positive correlation
perfect negative correlation
Answer:
High positive correlation
Step-by-step explanation:
Perfect correlation is 1 or -1(0 is no correlation), the correlation coefficient is .8
It is positive because it is a positive number (closest to positive 1).
This value is close to 1 so it's a high positive correlation.
Answer:
Answer Is C.
Step-by-step explanation:
A cafeteria manager can choose from among six side dishes for the lunch menu: applesauce, broccoli, corn, dumplings, egg
rolls, or French fries. He uses a computer program to randomly select three dishes for Monday's lunch.
What is the theoretical probability that applesauce and broccoli will both be offered on Monday?
Answer:
20% it would be 10% if there was 10 items. 5 items mean every item has 20%.
Step-by-step explanation:
Answer: 0.20
Step-by-step explanation:
Given : The number of side dishes for the lunch menu =6
The number of ways to select 3 dishes from 6 :
Total outcomes : [tex]^6C_3=\dfrac{6!}{3!(6-3!)} \ \ [\because\ ^nC_r=\dfrac{n!}{r!(n-r)!}\ ][/tex]
If applesauce and broccoli is already selected , then we need to select only one dish out of remaining 4 dishes.
Number of ways to select 1 dish from 4 :
Favorable outcomes: [tex]^4C_1=\dfrac{4!}{1!(4-1)!)}=4[/tex]
Now, the theoretical probability that applesauce and broccoli will both be offered on Monday :-
[tex]\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}\\\\=\dfrac{4}{20}=0.20[/tex]
Hence, the theoretical probability that applesauce and broccoli will both be offered on Monday = 0.20
Questões matemáticas
4) 3a- 4b ( 4 - 7a + 2b ) + b
6) 3mn ( m² + n² - m + 4n - 5 )
8) ( x + √5 )²
9) ( 4x + 2y )²
10) (2w-1,6)²
13) (x+11)(x+18)
15) (x+4,7)(x+3,25)
Considere x=-4, y=48 e z=2,7
17) 2x-y+3z
18) xz+1,57
20) x³+2x²-4x
Need Help:> :> ^^^^^^^^^
Multiply the numbers by 2
7*2=14
14*2= 28
28*2=56
Answer is 56
ANSWER
56
EXPLANATION
We want to find the next number in the sequence,
7,14,28,
Observe that, there is a common ratio of 2 among the terms.
That is ,
7(2)=14
14(2)=28
Therefore the next term is
28(2)=56
Therefore the number that goes into the box is 56.
The solution to x2 – 10x = 24 is
Answer:
x = - 2, x = 12
Step-by-step explanation:
Given
x² - 10 x = 24 ( subtract 24 from both sides )
x² - 10x - 24 = 0 ← in standard form
To factorise the quadratic
Consider the factors of the constant term (- 24) which sum to give the coefficient of the x- term (- 10)
The factors are - 12 and + 2, since
- 12 × 2 = - 24 and - 12 + 2 = - 10, thus
(x - 12)(x + 2) = 0
Equate each factor to zero and solve for x
x - 12 = 0 ⇒ x = 12
x + 2 = 0 ⇒ x = - 2
The solution of this quadratic equation to x² – 10 x = 24 is x = - 2 & x = 12
What is a quadratic equation?A quadratic is a sort of problem that deals with a variable accelerated by using an operation called squaring. This language derives from the area of a rectangular being its facet period expanded with the aid of itself. The phrase "quadratic" comes from quadrant, the Latin word for square.
x² – 10 x = 24
⇒ x² +2X -12X -24 = 0
⇒ x (x - 2) -12(x - 2) =0
⇒ x = 12 OR ( x = -2)
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For which value of 0 is sin0=-1:
A. Pi/2
B. Pi
C. 3Pi/2
D. 2Pi
Answer:
C. 3Pi/2 or 270 degrees
Step-by-step explanation:
The first step is to ignore the negative sign and then evaluate the arcsin of 1 to obtain the reference angle of θ in the first quadrant;
θ = arcsin(1)
θ = 90 degrees or equivalently pi/2
Since the sine of θ was given as -1, this will imply that θ lies either in the third or forth quadrant where the sine of an angle is negative.
To obtain the value of θ in the third quadrant we simply add 180 degrees of pi radians to our reference angle;
90 + 180 = 270 degrees
pi/2 + pi = 3/2 pi
What is the median of the data set:
4, 5, 9, 2, 7, 4, 3, 11
a 4
b 4.5
c 5
d 9
Answer:
4.5
Step-by-step explanation:
because 2 3 4 4 5 7 9 11
4.5 is the middle number, between 4 and 5 since you find what the middle number is
Here is some fun:
[tex]mean=\frac{\Sigma_{0}^{n}a_r}{n}=\frac{a_0+a_1+\dots+a_{\infty}}{\infty}[/tex]
[tex]
mean=\frac{4+5+9+2+7+4+3+11}{8}=\frac{45}{8}=\boxed{5.625}
[/tex]
And now the real work:
[tex]median=\frac{2+7}{2}=\boxed{4.5}[/tex]
The answer is B. 4,5
Hope this helps.
r3t40
use the associative property of addition to find the total of 1,10, and 18 in two different ways.
Answer:
(1+10)+18=11+18=29; 1+(10+18)=1+28=29
Step-by-step explanation:
the associative property of addition means that no matter in what order you group the numbers for addition the results come out to be the same.
using the associative property of addition to find the total of 1,10, and 18 in two different ways
first: (1+10)+18
=11+18
=29
second: 1+(10+18)
=1+28
=29!
What the equation for a slope of 3 and y-intercept of (0,-2)
The answer is y = 3x - 2
Y=3x-2
The formula y=mx+b is the slope intercept formula. You would enter the information of the problem into the equation.
You would place the slope in the place of m and the y intercept in the place of b.
Since it is a negative slope it would be -2 instead of +2 if it was positive.
if you flip a fair coin 5 times, and see 3 heads and 2 tails, what fraction of the time will you expect to see a head on the sixth flip
A:1/64
B:1/2
C:3/5
D:2/3
E:5/6
I hope I'm not wrong here, but B.1/2? Only because its a 50% chance
The fraction of the time will you expect to see a head on the sixth flip will be 1/2.
What is probability?Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Here the sample variables are = [3 heads , 2 tails]
The number of the times coin flipped = 6 times
Probability of the flipping the coin and having head will be
P(A)=3/6=1/2
Hence the fraction of the time will you expect to see a head on the sixth flip will be 1/2.
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Kylie needs to pack her baton for a color-guard competition. The baton is 38 inches long. Will it fit in a rectangular box with a base of 13 inches by 35 inches and a height of 13 inches?
What is the diagonal??
HELP ASAP
Quiz is tmmr
Answer:
The diagonal is 39.54 in
Step-by-step explanation:
First we use the Pythagorean theorem to calculate the length of the diagonal of the base.
If the base measures 13 inches by 35 inches then the diagonal is:
[tex]c = \sqrt{13^2 +35^2}\\\\c= 37.34\ in[/tex]
Now we use the Pythagorean theorem again to find the diagonal of the cube.
If the height of the box is 13 inches and the diagonal of the base is 37.34 inches then the diagonal of the cube will be
[tex]z = \sqrt{37.34^2 +13^2}\\\\z= 39.54\ in[/tex]
The baton will fit in the box if it is placed in the direction of the diagonal of the cube, since:
39.54\ in > 38 inches
Using the 3D Pythagorean theorem, the diagonal of the box is calculated to be approximately 39.53 inches, which means that Kylie's 38-inch baton will fit inside the box diagonally.
Explanation:Kylie needs to check if her 38-inch long baton will fit diagonally in a box with dimensions of 13 inches by 35 inches by 13 inches. To determine whether the baton will fit, she needs to find the length of the longest diagonal of the box. This is solved by using the 3D Pythagorean theorem, which is an extension of the traditional Pythagorean theorem applied to three dimensions.
To find the length of the diagonal (d), we use the formula:
d = √(l² + w² + h²)
Where l is the length, w is the width, and h is the height of the box. Substituting the given values:
d = √(13² + 35² + 13²)
d = √(169 + 1225 + 169)
d = √1563
d ≈ 39.53 inches
The calculated diagonal length of approximately 39.53 inches indicates that Kylie's baton, which measures 38 inches, will indeed fit inside the box diagonally.
what is 10n+2=7n+14
Answer:
n = 4
Step-by-step explanation:
Given
10n + 2 = 7n + 14
Collect terms in n on the left side and numbers on the right side
Subtract 7n from both sides
3n + 2 = 14 ( subtract 2 from both sides )
3n = 12 ( divide both sides by 3 )
n = 4
Answer n=4
Step-by-step explanation: Collect the like terms 10n-7n=14-2
3n=12 divide both sides by 3
Which expression is equivalent to 64y^18-1000z^6?
The expression (4y^6)^3 - (10z^2)^3 is equivalent to 64y^18 - 1000z^6.
Explanation:Factor out common powers:
64y^18 = (2^6)(y^3)^6
1000z^6 = (10^3)(z^2)^3
Rewrite the expression with factored terms:
64y^18 - 1000z^6 = (2^6)(y^3)^6 - (10^3)(z^2)^3
Apply power of a power rule:
(a^m)^n = a^(mn)
(2^6)(y^3)^6 = 2^(66) * y^(36) = 2^36 * y^18
(10^3)(z^2)^3 = 10^(33) * z^(2*3) = 10^9 * z^6
Substitute back the simplified terms:
2^36 * y^18 - 10^9 * z^6 = (4y^6)^3 - (10z^2)^3
Therefore, (4y^6)^3 - (10z^2)^3 is the equivalent expression to 64y^18 - 1000z^6. Both expressions involve the difference of cubes of binomials, with one focusing on powers of 4y^6 and the other emphasizing powers of 10z^2.
Need Help Fast !!!!!!!!!!!!!!!!
-10t+6=-44
-10t=-50
t= 5
ANSWER
[tex]h(5) = - 44[/tex]
EXPLANATION
The given expression is :
h(t)=-10t+6
We want to find the value of t that will evaluate to -44.
We equate the function to -44 and solve for t.
[tex]-10t+6 = - 44[/tex]
Subtract 6 from both sides of the equation,
[tex]-10t = - 44 - 6[/tex]
[tex]-10t = - 50[/tex]
Divide both sides by -10
[tex]t = 5[/tex]
Which value of m satisfies the inequality 170 − 7m > 99?
Answer:
[tex]\large\boxed{m<\dfrac{71}{7}\to\left\{m\ |\ m<\dfrac{71}{7}\right\}\to m\in\left(-\infty,\ \dfrac{71}{7}\right)}[/tex]
Step-by-step explanation:
[tex]170-7m>99\qquad\text{subtract 170 from both sides}\\\\-7m>-71\qquad\text{change the signs}\\\\7m<71\qquad\text{divide both sides by 71}\\\\m<\dfrac{71}{7}[/tex]
10 because if you minus 170 from 10 it would still be less than 99
8.
If a principal of $2500 was invested at a rate of 5% compounded semiannually and terminates
with a balance of $5509.39, how long was the money invested for? hint: use table A11 or log calculations
4 yrs
8 yrs
16 yrs
32 yrs
Answer:
The money was invested for 16 years
Step-by-step explanation:
This is a compound interest problem and the following information has been provided;
Principal, P = 2500
Rate, r = 0.05 compounded semiannually. This will imply an effective rate of 0.05/2 = 0.025 effective per semiannual period.
Accumulated amount, A = 5509.39
We are required to determine the duration of investment in years. We let the number of years be n. We then use the compound interest formula;
[tex]A=P(1+r)^{n}\\\\5509.39=2500(1+0.025)^{2n}[/tex]
We raise to power 2n since there are 2n semiannual periods in n years. The next step is to divide both sides by 2500;
[tex]2.203756=1.025^{2n}\\[/tex]
We introduce logs in order to solve for n;
[tex]ln(2.203756)=2nln(1.025)\\\\2n=\frac{ln(2.203756)}{ln(1.025)}\\ \\2n=32\\\\n=16[/tex]
Identify the asymptotes of y = 3/x +2.
Answer:Vertical Asymptotes: x=0
Horizontal Asymptotes: y=2
Here’s a graph picture...
If a 30% discount is put on an item, and the sale price is $206.50, then what was the original price?
Answer:
295
Step-by-step explanation:
.3 x 295 = 88.5
295 - 88.5 = 206.5
The cost in dollars, y, of a large pizza with x toppings from Pat’s Pizzeria can be modeled by a linear function. A large pizza with no toppings costs $14.00. A large pizza with 2 toppings costs $17.50.
What is the cost of a pizza with 5 toppings? Round to the nearest penny.
$22.75
Start by finding the cost of each topping. Subtract $17.50 minus $14.00 to find that adding 2 toppings costs $3.50. Now, divide $3.50 by 2 to find that the cost for adding only one topping is $1.75.
Then, multiply $1.75 by 5 to find how much it costs to add 5 toppings. You get $8.75.
Finally, add the cost of 5 toppings to the cost of a large pizza with no toppings. $14.00 plus $8.75 equals $22.75, so a large pizza with 5 toppings costs $22.75.
Answer: $22.75
Step-by-step explanation:
Given : The cost in dollars, y, of a large pizza with x toppings from Pat’s Pizzeria can be modeled by a linear function.
A linear function is given by :-
[tex]y=mx+c[/tex] (1)
, where m is slope (rate of change of y w.r.t x) and c is the y-intercept.
A large pizza with no toppings costs $14.00.
i.e. for x=0 , y= 14
Put theses values in (1) , we get
[tex]14=m(0)+c\\\Rightarrow\ c=14[/tex] (2)
A large pizza with 2 toppings costs $17.50.
i.e. for x=2 , y= 17.50
Put theses values in (1) , we get
[tex]17.50=m(2)+c[/tex]
Put value of c from (2)
[tex]17.50=2m+14\\\\[/tex]
Subtract 14 from both sides , we get
[tex]3.50=2m[/tex]
Divide both sides by 2 , we get
[tex]1.75=m[/tex]
Put m= 1.75 and c= 14 in (1) , the linear function representing cost of large pizza becomes [tex]y=1.75x+14[/tex]
At x= 5
[tex]y=1.75(5)+14=8.75+14=22.75[/tex]
Thus , the cost of a pizza with 5 toppings= $22.75
CAN ANYONE HELP ME WITH THIS
The line in the middle has a right angle, so the angle just above the Y would be 90 degrees.
The angle to the right of y is given as 48.
The three inside angles of a triangle need to equal 180.
So y = 180 - 90 - 48 = 42 degrees.
a number c increased by 17
c increased by 17
Increased = +
c + 17 is the answer
Answer:
Error question or wrong
1. What is the value of x in the figure?
2. What is the value of y in the figure?
3. What is the value of z in the figure?
Answer:
[tex]x=6\sqrt{5}\\ \\y=3\sqrt{5}\\ \\z=6[/tex]
Step-by-step explanation:
The height of the right triangle drawn to the hypotenuse is geometric mean of two segments of hypotenuse, so
[tex]z^2=12\cdot 3\\ \\z^2=36\\ \\z=6[/tex]
By the Pythagorean theorem,
[tex]x^2=12^2+z^2\\ \\x^2=144+6^2\\ \\x^2=144+36\\ \\x^2=180\\ \\x=6\sqrt{5}[/tex]
and
[tex]y^2=z^2+3^2\\ \\y^2=6^2+9\\ \\y^2=36+9\\ \\y^2=45\\ \\y=3\sqrt{5}[/tex]
if 1/4
inch equals 50 miles, find the miles represented by 4 1/2
inches.
Answer:
900 miles
Step-by-step explanation:
Well, 200 miles is 1 inch. 100 miles is 1/2 an inch.
Answer:
900
Step-by-step explanation:
Given: 1/4 in. = 50 miles
Find the amount of miles per inch. Multiply 4 to both sides of the equation.
(1/4 in.) x (4) = (50 miles) x (4)
4/4 in. = 200 miles
1 in. = 200 miles
Now, find the amount of miles for 4 1/2 in. Multiply 4 1/2 to both sides.
Note that 4 1/2 = 4.5
(1 in.)(4.5) = (200 miles) x (4.5)
4.5 = 200 x 4.5
4.5 = 900
900 miles is your answer.
~
Find the volume of a sphere with a diameter of 13 in. Round your answer to the nearest cubic inch. Use pi=3.14
A. 9,198 in^3
B. 862 in^3
C. 1,150 in^3
D. 287 in^3
Answer: C.
Step-by-step explanation:
Diameter = Radius/2
So, the radius would be 6.5 in.
The formula for the volume of a sphere is: V = 4/3 (3.14) r^3.
So, once you "plug in" the radius, you get an equation of V = 4/3 (3.14) r^3.
And, once you solve the equation, you get and answer of 1,150 in.^3, rounded to the nearest cubic inch.
The volume of a sphere with a diameter of 13 inches, using the formula V = 4/3 * π * r³ and rounding off to the nearest cubic inch, is approximately 1151 cubic inches or choice C, 1150 in³.
Explanation:To find the volume of a sphere, you can use the formula V = 4/3 * π * r³, where V is the volume and r is the radius. In this case, the diameter of the sphere is given as 13 inches. So, the radius would be half the diameter, which is 6.5 inches.
Plugging the values into the formula, we get V = 4/3 * 3.14 * (6.5)³. Calculating this gives an approximate value of 1151 cubic inches. Since we need to round to the nearest cubic inch, the final volume is 1151 in³.
So, the correct choice is C. 1150 in³.
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