Answer:
[tex]7\sqrt{2} \ cm[/tex]
Step-by-step explanation:
Formula ………………………………………………
The length of a diagonal of a square with side of length “a” is :
[tex]a\sqrt{2}[/tex]
======================================================
Since a = 7 (in our case) then
[tex]\text{the length of the diagonal} =7\sqrt{2}[/tex]
Note : you can also use the Pythagorean theorem.
PLEASE HELP WILL GIVE BRAINLIEST!
Evaluate for f(6), show all your work: f(x)=x^2-4
Answer: 32
Step-by-step explanation:
f(6) = 6^2-4 = 36-4 = 32
At the beginning of the year, Cassandra talks to her cousin about a $1000 loan which she will repay after she graduates from college. On December 31st, her cousin will add 12% interest to the balance of the loan outstanding. If Cassandra makes no payments on the loan until she graduates, which equation shows the loan balance b after n years?
Using an exponential function, it is found that the loan balance b after n years is given by:
[tex]b(n) = 1000(1.12)^n[/tex]
What is an exponential function?An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
A(0) is the initial value.r is the growth rate, as a decimal.In this problem, we have that:
She took a $1,000 loan, hence A(0) = 1000.The interest rate is of r = 0.12.Hence the balance b after n years is given by:
[tex]b(n) = 1000(1.12)^n[/tex]
More can be learned about exponential functions at https://brainly.com/question/24372153
#SPJ1
the nearest known exoplanet from earth is 4.25 light years away .how many km is this? give your answer in standard form
Answer:
4.021 × 10¹³ km
Step-by-step explanation:
The conversion factor of light years to km is;
1 light year = 9.461 × 10¹² km
Thus;
4.25 light years = 4.25 × 9.461 × 10¹² km = 4.021 × 10¹³ km
A ball is thrown upward from a height of 15 ft with an initial velocity of 5 ft/s. Use the equation h=-16t^2+5t+15 to answer the following questions. Round to the nearest tenth.
How long will it take for the ball to hit the ground (h=0)?
What is the height of the ball after 0.5 seconds?
Answer:
1) 1.1 seconds
2) 13.5 feet
Part A[tex]\rightarrow \sf -16t^2 + 5t + 15 = 0[/tex]
Apply quadratic formula:
[tex]\rightarrow \sf t= \dfrac{-5\pm \sqrt{5^2-4\left(-16\right)\cdot \:15}}{2\left(-16\right)}[/tex]
Simplify following
[tex]\rightarrow \sf t=-\dfrac{-5+\sqrt{985}}{32},\:t=\dfrac{5+\sqrt{985}}{32}[/tex]
In decimal form:
[tex]\rightarrow \sf t=-0.825 ,\:t=1.137[/tex]
Conclusion:
As time is be only positive: t = 1.1 seconds
Part B
[tex]\rightarrow \sf h=-16t^2 + 5t + 15[/tex]
insert t = 0.5
[tex]\rightarrow \sf h=-16(0.5)^2 + 5(0.5) + 15[/tex]
simplify
[tex]\rightarrow \sf h=13.5[/tex]
Express sin(-184) as a function of a positive acute angle.
The sin(-184) can be expressed as cos 86° as a function of a positive acute angle.
How do you express a trigonometry function as a positive acute angle?
To express a trigonometry identity as a function of a positive acute angle, we need to find the quadrant in which that given identity is located.
Here, we have a negative trigonometry identity: Sin (-184)
Recall that:
the sine is negative in the third quadrant(III)So, to turn that to a positive sign, we add 360
=sin(-184 + 360)
= sin(176)
To find the positive acute angle, we have:
x = cos(176 - 90)
x = cos 86°
Therefore, we can conclude that the sin(-184) can be expressed as cos 86° as a function of a positive acute angle.
Learn more about trigonometry identities here:
https://brainly.com/question/7331447
#SPJ1
Find the values of x and y.
Answer: x=60°, y=60°
Step-by-step explanation:
because they are equilateral triangles, which the angles are all 60° Please correct me if I’m wrong, but I’m quite sure.
help me please i don't understand
The depth of the water at the deepest point in the waterslide and to the nearest hundredth of a meter is approximately 0.19 meters. (Correct choice: A)
How to determine the depth of the water in a waterslide
In this question we should apply the concepts of right triangles and trigonometric functions to determine the height of the water within the waterslide. A geometric diagram of the cross section of the waterslide is presented below, which indicates the existence of circular symmetry.
Now we proceed to determine the height of the water:
cos α = (0.5 m/0.75 m)
α ≈ 48.190°
y = (0.75 m) · sin 48.190°
y = 0.559 m
x = 0.75 m - 0.559 m
x = 0.191 m
The depth of the water at the deepest point in the waterslide and to the nearest hundredth of a meter is approximately 0.19 meters. (Correct choice: A)
To learn more on trigonometry: https://brainly.com/question/22698523
#SPJ1
thera are 672 eggs in 6 identical boxes
a. How many eggs are in each box?
b. many eggs are edible if half of the eggs are bad?
Answer:
112 are in each box
336 are edible
Step-by-step explanation:
672÷6= 112
672÷2= 336
On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (negative 2, 3) and (0, negative 1). Everything to the left of the line is shaded. The second dashed line has a negative slope and goes through (0, 2) and (1, 0). Everything to the right of the line is shaded.
Which inequality pairs with y≤−2x−1 to complete the system of linear inequalities represented by the graph?
y<−2x+2
y>−2x+2
y<2x−2
y>2x−2
Answer:
To graph the inequality
y < 2x - 5
we graph the dashed boundary line y=2x-5 with a positive slope of 2 and y-intercept (0,-5) and shade everything to the right.
To graph the inequality y>-3x+1, we graph the dashed boundary line y=-3x +1 with y-intercept (0,1) and shade every above it.
The intersection of the two shadings is the solution to the system of inequalities:
y < 2x - 5
and
y > -3x + 1
19. Solve the following inequality.
Answer:
c
Step-by-step explanation:
(5y - 1) = 4y + (9y - 4) = 5y
2y > .75
Answer:
C. The solution set is {y|y > 0.75}.
Step-by-step explanation:
Given :
5y - 1 < 9y - 4Add 4 to each side.
5y - 1 + 4 < 9y - 4 + 45y + 3 < 9ySubtract 5y from each side.
5y + 3 - 5y < 9y - 5y4y > 3y > 3/4y > 0.75Solution set
C. The solution set is {y|y > 0.75}.
Jason cycles 14.5 km in 50 min. Express his speed in km/h.
Answer:
i got 17.4km/H pretty sure im right
What is the product of (4y - 5) (3y - 7)?
Answer
(12y-35)
(4yx3y-5x7)
Answer:
12y² - 43y + 35
Step-by-step explanation:
Multiply each term of the first binomial by each term of the second binomial. Then combine like terms.
(4y - 5)(3y - 7) =
= 4y × 3y + 4y × (-7) + (-5) × 3y + (-5) × (-7)
= 12y² - 28y - 15y + 35
= 12y² - 43y + 35
jacob has 96 books to stack on library shelves. each half can hold 9 books.how many shelves will he need to stack all his books
Answer:
11 shelves.
Divide 96 by 9
96 ÷ 9 = 10.6
Since 10.6 rounds to 11, and it is more than 10, we will need 11 shelves to store the books, since there is no such thing as a half-bookshelf here.
[tex]\huge\color{yellow}\underline \colorbox{violet} {\color{red}{QUESTION}}[/tex]
in the pic
Need done by tonight please! Will mark brainliest just need it done.
Answer:
1. Binary number system only uses 2 digits: 0 and 1.
2. Octal number system uses 8 digits: 0,1,2,3,4,5,6,7 with the base of 8.
3. Decimal number system uses 10 digits: 0,1,2,3,4,5,6,7,8,9 with a base of 10.
4. Hexadecimal number system uses 16 digits and alphabets: 0,1,2,3,4,5,6,7,8,9 and A,B,C,D,E,F with the base of 16.
5. Quinary number system uses 0,1,2,3,4 with 5 as the base.
Absolute value is a number's distance from 0 on the number line.
A prime factor is a number with no factors other than one and itself.
The smallest quantity divisible by every number of the set is known as the least common multiple.
The denominator of a fraction can never be zero since a number divided by zero is not defined.
If the numerator is greater than or equal to the denominator, the fraction is called an improper fraction.
A mixed fraction is the sum of a whole number and a fraction.
To simplify a fraction is to convert it into a form which the numerator and denominator have no common factor other than one.
Step-by-step explanation:
Hope this helps :)
What is the solution set of y = x2 2x 7 and y = x 7? a. {(0, 7), (-1, 6)} b. {(0, 7), (-7, 0)} c. {(0, 7), (1, 8)} d. {(-2, 0), (4, 0)}
The solution set of the equation is (0, 7)(-1, 6)
y = x² + 2x + 7
y = x + 7
How to find the solution of an equation sets?
y = x² + 2x + 7
y = x + 7
x² + 2x + 7 = x + 7
x² + 2x - x + 7 - 7 = 0
x² + x = 0
x(x + 1) = 0
Therefore,
x = 0 and x = -1
Substitute the value in equation(ii)
when x = 0
y = x + 7
y = 0 + 7
y = 7
when x = -1
y = -1 +7
y = 6
Therefore, the solution set are (0, 7)(-1, 6)
learn more on equation set here: https://brainly.com/question/1502195
#SPJ4
Maria can stack a pile of wood in 20 minutes, and
alex can stack the same pile of wood in 12 minutes.
how long will it take them both working together
to stack the same pile of wood?
Answer:
7.5 minutes
Step-by-step explanation:
The stacking rate working together is assumed to be the sum of the separate stacking rates. The rates are given in terms of minutes per pile, but we need to do the computation with rates in terms of piles per minute.
__
total rate = Maria's rate + Alex's rate
= 1/20 piles/min + 1/12 piles/min = (12 +20)/(20·12) piles/min
= 32/240 piles/min = 2/15 piles/min
Then the rate in terms of minutes per pile is ...
1/(2/15 piles/min) = 15/2 min/pile = 7.5 min/pile
When both work together, it will take them 7.5 minutes to stack a pile of wood.
who can help me finish a course on edge ive done half of the course already its algebra !!
Sure, post the questions.
Please help asap
Multiply:
3(4a)
Will give 25 points!
Answer:
12a
Step-by-step explanation:
If I'm understanding your question correctly, 3(4a), or 3 × (4a), is simply 12a.
Answer: 12a
Step-by-step explanation:
Multiply:
3(4a)
⇒3 × 4a
⇒12a Answer
hope that helps...
The net of a cone is composed of a circle and a
triangle
wedge
triangle
Answer:
I would say triangle. But I am not completely sure!
Step-by-step explanation:
Hope this helps!
Answer:Triangle
Step-by-step explanation:
What is the volume of a sphere with a radius of 6 mm? sphere v = four-thirds pi r cubed v = 216pi mm3 v = 288pi mm3 v = 512pi mm3 v = 648pi mm3
Answer:
[tex]V =288 \pi \ mm^3[/tex]
Step-by-step explanation:
[tex]V =\frac{4}{3} \pi r^{3}[/tex]
[tex]=\frac{4}{3} \pi \left( 6\right)^{3}[/tex]
[tex]=\left( \frac{4}{3} \right) \times \pi \times 216[/tex]
[tex]=\left( \frac{4}{3} \right) \times 216\times \pi[/tex]
[tex]=288\times \pi[/tex]
Answer:
IT IS B
Step-by-step explanation:
SOURCE: TRUST ME BRO
A frog wants to cross a stream. The stream is two metres wide. On every jump, Frog covers one-third metre distance. In how many jumps will Frog reach from rock A to rock B?
1/3 of 2 meters = 66.668 x 3 = 200.004
Drag the tiles to the correct boxes to complete the pairs.
Simplify the inequalities and match them with the graphs that represent them.
Answer:
1) 1, 2) 3, 3) 2, 4) 4Step-by-step explanation:
Solve the inequalities and match with the graphs
1) 7x < 42 ⇒ x < 42/7 ⇒ x < 6 ⇔ matching the graph 12) 3x > 15 ⇒ x > 15/3 ⇒ x > 5 ⇔ matching the graph 33) x + 1 < 8 ⇒ x < 8 - 1 ⇒ x < 7 ⇔ matching the graph 24) 2x > 12 ⇒ x > 12/2 ⇒ x > 6 ⇔ matching the graph 4Answer:
7x < 42
x + 1 < 8
3x > 15
2x > 12
Step-by-step explanation:
> means "more than" (shading to the right)
< means "less than" (shading to the left)
Solve the given inequalities
7x < 42
⇒ 7x ÷ 7 < 42 ÷ 7
⇒ x < 6
An open circle on 6, shading to the left
3x > 15
⇒ 3x ÷ 3 > 15 ÷ 3
⇒ x > 5
An open circle on 5, shading to the right
x + 1 < 8
⇒ x + 1 - 1 < 8 - 1
⇒ x < 7
An open circle on 7, shading to the left
2x > 12
⇒ 2x ÷ 2 > 12 ÷ 2
⇒ x > 6
An open circle on 6, shading to the right
Can someone help please
Answer:
The answer is 2 -option b
Answer:
B) 2
6²(6 × 6) = 36
Write the quotient in repeated multiplication form. Then write the quotient as a power.
The quotient as repeated multiplication is
The quotient as a power is
The expression written as a product is:
[tex](-4.5)^6*(-4.5)^{-2}[/tex]
And written as a power:
[tex](-4.5)^4[/tex]
How to rewrite the expression?Here we need to remember the two rules:
[tex]a^n = \frac{1}{a^{-n}}[/tex]
[tex]a^n*a^m = a^{n + m}[/tex]
Using the first one, we can write the quotient as a product:
[tex]\frac{(-4.5)^6}{(-4.5)^2} = (-4.5)^6*(-4.5)^{-2}[/tex]
Now we can use the second property to write the expression as a single power, we will get:
[tex]\frac{(-4.5)^6}{(-4.5)^2} = (-4.5)^6*(-4.5)^{-2} = (-4.5)^{6 - 2} = (-4.5)^4[/tex]
If you want to learn more about powers:
https://brainly.com/question/8952483
#SPJ1
Which equation represents the parabola shown on the graph?
O y2 = -2x
O y² = -8x
O x² = -2y
O x² = -8y
The equation that represents the horizontal parabola given on the graph is:
y² = -8x
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
x = a(y - k)² + h
In which a = 1/p is the leading coefficient.
In this problem, the vertex is (0,0), hence h = k = 0, and:
ay² = x.
The directrix is at x = 2, and the parabola opens left, hence:
p = -4(2 - 0) = -8.
Hence the equation is:
y² = px = -8x.
More can be learned about the equation of a parabola at https://brainly.com/question/24737967
#SPJ1
How many meters is this?
Answer:
6.28 meters
Step-by-step explanation:
Circumference is the distance around the circle, given by:
C = pi•d
C = 3.14 • 2
C = 6.28 meters
Answer:
6.28 Meters
Step-by-step explanation:
2pi * r
= 2*3.14
= 6.28 Meters
1, 2, 2, 3, 4, 6, 8, 9, 10
What is the median?
Answer:
4
Step-by-step explanation:
Mean (Average) 5
Median 4
Range 9
Mode 2, appeared 2 times
Geometric Mean 3.8971508839086
Largest 10
Smallest 1
Sum 45
Count 9
Sorted Data Set: 1, 2, 2, 3, 4, 6, 8, 9, 10
What is the volume of a sphere with a diameter of 32.5 m, rounded to the nearest tenth of a cubic meter?
Answer:
17965.1
Step-by-step explanation:
Formula: V = 4/3 pi r^3
r = d/2
r = 32.5/2
r = 16.25
V = 4/3 * 3.14 * (16.25)^3
V = 17965.05 to the nearest tenth is
V = 17965.1
Enrique is saving money to buy a graphing calculator. So far he has saved $30.
His math teacher told him he has saved 40% of what he will need. How much
does the calculator cost?
Answer: its free
Step-by-step explanation: