Using the "fives fact" (5 x 6 = 30) as a starting point, we added one more group of 6 to reach the final result of 36.
To use the "fives fact" to solve 7 x 6, we can break it down into simpler calculations using the fact that 5 x 6 = 30.
Here's the step-by-step calculation:
1. Start with the "fives fact": 5 x 6 = 30.
2. Since we need to find 7 x 6, we can add another 6 to the result of 5 x 6:
30 + 6 = 36
Therefore, 7 x 6 equals 36.
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How many oz. of a metal containing 40%
gold must be combined with 7 oz. of a
metal containing 90% gold to form an
alloy containing 75% gold?
Answer:
3 oz
Step-by-step explanation:
Let x represent the number of oz. of the medal with 40% gold:
Set up an equation and solve for x:
0.4x + 7(0.9) = 0.75(x + 7)
0.4x + 6.3 = 0.75x + 5.25
6.3 = 0.35x + 5.25
1.05 = 0.35x
3 = x
So, you will need 3 oz. of the metal with 40% gold
Example 3.7.4: The sum of two positive numbers is 16. What is the smallest possible value of the sum of their squares
Answer:
The smallest possible value of the sum of their squares is 128.
Step-by-step explanation:
Let the first number = x
let the the second number = y
x + y = 16
y = 16 -x
minimum value, f = x² + y²
f(x) = x² + (16-x)²
f(x) = x² + 256 - 32x + x²
f(x) = 2x² - 32x + 256
f(x)' = 4x - 32
4x - 32 = 0
4x = 32
x = 32 / 4
x = 8
The absolute minimum value of x = 8
y = 16 - x
y = 8
The smallest possible value of the sum of their squares is given by x² + y²;
= (8)² + (8)²
= 128
Therefore, the smallest possible value of the sum of their squares is 128.
Solve each system of equations algebraically x-y=6 y=-1
Answer:
x-(-1)=6
-x=6
-x/-1 6/-1
x=-6
Answer:
Therefore, the solution of the system of equations will be:
[tex]x=5,\:y=-1[/tex]
Step-by-step explanation:
Given the system of equations
[tex]x-y=6;\:y=-1[/tex]
solving
[tex]\begin{bmatrix}x-y=6\\ y=-1\end{bmatrix}[/tex]
[tex]\mathrm{Subsititute\:}y=-1[/tex]
[tex]\begin{bmatrix}x-\left(-1\right)=6\end{bmatrix}[/tex]
[tex]\begin{bmatrix}x+1=6\end{bmatrix}[/tex]
Isolate x for [tex]x+1=6[/tex]
[tex]x+1=6[/tex]
[tex]x=5[/tex]
Therefore, the solution of the system of equations will be:
[tex]x=5,\:y=-1[/tex]
Solve 2x^2 - 3x = 12 using the quadratic formula.
A) x = 3/4+√105/4i, x = 3/4-√105/4i
B) x = 3/4+√87/4i, x = 3/4-√87/4i
C) x = 3/4 + √87/4, x = 3/4-√87/4
D) x = 3/4 + √105/4, x = 3/4-√105/4
Answer:
[tex]x = \frac{3}{4} + \frac{ \sqrt{105} }{4} \: \: , \: \: \: x = \frac{3}{4} - \frac{ \sqrt{105} }{4} \\ [/tex]
Step-by-step explanation:
2x² - 3x - 12 = 0
Using the quadratic formula which is
[tex]x = \frac{ - b \pm\sqrt{ {b}^{2} - 4ac} }{2a} \\ [/tex]
From the question
a = 2 , b = - 3 , c = - 12
So we have
[tex]x = \frac{ - - 3\pm \sqrt{ ({ - 3})^{2} - 4(2)( - 12)} }{2(2)} \\ = \frac{3\pm \sqrt{9 + 96} }{4} \\ = \frac{3\pm \sqrt{105} }{4} \: \: \: \: \: \: [/tex]
Separate the solutions
We have the final answer as
[tex]x = \frac{3}{4} + \frac{ \sqrt{105} }{4} \: \: , \: \: \: x = \frac{3}{4} - \frac{ \sqrt{105} }{4} \\ [/tex]
Hope this helps you
Jane has 34 candles leftover from the last craft show and Brianna
has 2 candles. They are making more candles for the next show.
Jane makes 24 candles per hour and Brianna makes 32 candles per
hour. They are also going to use the candles left over from the last
show and want to have the same number of candles at their stalls for
this show. Let h represent the number of hours they need to work
for this.
Answer:
4 hours
Step-by-step explanation:
Given that the number of leftover candles for Jane = 34
and the number of leftover candles for Brianna = 2
Rate of candle making for Jane = 24 candles/ hour
Rate of candle making for Jane = 32 candles/ hour
As they work for h hours to make candles.
So, in h hours, the number of new candles made by Jane = 24h candles
For Jane, the total number of candles after h houres, including the leftover candles [tex]= 24h+34 \cdots(i)[/tex]
Similarly, in h hours, the number of new candles made by Brianna = 32h candles
For Brianna, the total number of candles after h houres, including the leftover candles [tex]= 32h+2 \cdots(ii).[/tex]
As they want to have the same number of candles at their stalls, so equating the numbers of candles from equations (i) and (ii), we have
[tex]24h+34=32h+2 \\\\\Rightarrow 32h-24h=34-2 \\\\\Rightarrow 8h=32\\\\[/tex]
[tex]\Rightarrow h=32/8=4[/tex] hours.
Hence, both need to work for 4 hours to have the same number of candles.
The completely factored form of z^5 + 4z^4 - 12z^3
Answer:
−108z 5−64z 3+3z 2−24z−384/6
Step-by-step explanation:i just looked it up.
7 large tanks and 40 fish in each tanks how many fish on display
Answer:
280
Step-by-step explanation:
All you have to do is 7x4 and look for how many 0's there are in the equation and add them on.
If a snail travels at a rate of of a mile every of an hour,
what is the unit rate in miles per hour?
Answer:
1mph or 1 mile per hour
Step-by-step explanation:
simple
What is the x-intercept of the graph of - x = 5?
Answer:
x=-5
Step-by-step explanation:
The x-intercept is x=-5
Answer:-5
Step-by-step explanation:If you draw out the graph, it would be a vertical line at the point -5. Since you are asking for the x intercept, it would be -5
pls help :( plssss plsss pls
Answer:
you can alwayd use desmos for graphing
5x-6y=-4
-6x+6y=-6
solve using elimination
HELP.
Answer:
x=10 y=9
Step-by-step explanation:
Write a integer for each situation. Explain the meaning of zero in each situation.
1. 3 miles below sea level
2. Earning $45
Point Q' is the image of Q(-7,-6) under the translation (x, y) + (x+12, y + 8).
What are the coordinates of Q'?
Answer:its b
Step-by-step explanation:i took the test
Write down step by step the process that you use
to solve multiplying a fraction by an integer.
Answer:
you place the 1 under the integer and follow the steps keep change it flip it . SO basically you keep the integer and the 1 and you change the sign to division and you place the numerator where the denominator is and the denominator goes where the numerator is.
Step-by-step explanation:
What is the value of a for the following circle in general form?
X^2+y^2+ax+by+c=0
Answer:
ANSWER: 8 A_P_E_X
Step-by-step explanation:
Plug the radius and the center point into the equation, and convert it to general form to get your answer.
The value of a is 4.
What is the standard equation of a circle?The standard equation of a circle is given by
(x -h)² + (y-k)² = r²
The equation given is
x² + y² +ax +by +c = 0
a = -h * 1
(h,k) represents the coordinate for the center of the circle
h = -4 , k =2
a = -(-4) *1 = 4
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Function f is defined by the equation f(x)=x2
What is f(3)
Help meeeeeee! If it’s correct you will get a something good!
Answer:
24/4=6
Step-by-step explanation:
In the model, there are 4 rows of 6 blocks. 24 total blocks divided by the 4 rows gives you six objects in each row.
HTH :)
Help please ASAP will mark brainliest!!
Answer:
y=4x-7
Step-by-step explanation:
y=4x+6 (1,-3)
y=mx+b
m= 4 (1,-3)
y-(-3)=4(x-1)
y+3=4x-4
-3 -3
y=4x-7
Pls help ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! pls
If you have 3 cups of pineapple juice, how many total cups of lunch can you make?
A motorboat moves across a lake. It begins at 50km from shore after 9 minutes it is 14 km from shore. What’s it’s distance from shore in a function
Answer:
List all of the solutions.
50 k m =
9 m i n u t e s =
14 k m =
Step-by-step explanation:
Answer:
y = -4x + 50
Step-by-step explanation:
To write the function we'll use y = mx + b, where y is the distance the boat is away from shore, m is how many km/minute the boat moves at, x is how many minutes it's been, and b is how many km away from shore the boat was at the start. We already know the value of b is 50, so we can put that into the equation:
y = mx + 50
To find how many km the boat moves per minute, let's use the given amount of minutes and km (9, 14) and put them into the equation:
14 = m(9) + 50
Now let's solve for m:
14 = 9m + 50
Subtract 50 from both sides to isolate the 9m:
14 - 50 = 9m + 50 - 50
- 36 = 9m
divide both sides by 9 to isolate the m:
-36/9 = 9m/9
-4 = m
The boat moves at -4 km/minute, which is the same thing as saying that after 1 minute passes, the boat gets 4km closer to the shore. Now we can input this value into the equation and we have our answer:
y = -4x + 50
2) f(x) = 27x^6+ 1524x^3+125
Answer:
Step-by-step explanation:
Let x^3 = y
f(x) = 27(x^3)^2 + 1524(x^3) + 125
f(x) = 27 y^2 + 1524y + 125
You can now put this into the quadratic formula. When you do, you get
(y + 0.0821)(y+56.3623) = 0
So now you substitute x^3 into this
(x^3 + 0.0821)(x^3 + 56.3623)
x^3 + 0.0821 = 0
x^3 = - 0.0821
cuberoot x^3 = cube root 0.0821
x = - 0.4346
x^3 = - 56.3623
x = - 3.8341
What's greater -5/7 or -2/7
I think -2/7.
-2/7 is closer to 0 which is neither positive nor negative.
-5/7 is closer to a whole negative number.
geometry is experienced that in the early childhood setting through
playing with blocks??
What is the slope of the line represented by the equation 3x+4y=12?
Answer:
-3/4
Step-by-step explanation:
3x+4y=12
-3x -3x
4y=-3x+12
÷4 ÷4
y=-3/4x+12
Answer:
-3/4 or -0.75
Example:
FIRST TO HELP IS BRAINLIEST
Answer:
(0,2)
Step-by-step explanation:
8.9 x 7 can u solve it with work shown
Answer:
62.3
Step-by-step explanation:
6
8.9
*7
____
62. 3
I tried to show how to do it but carry the 6 at the top
Answer:
64 (I rounded btw)
Step-by-step explanation:
8.9 × 7 = ??
1. Round 8.9
2. 8.9 can be rounded to 9
3. change equation
4. 9×7= 63
Thus, your answer is 63
(If your supposed to do the math differently tell me and I'll correct it)
On a coordinate plane, point B is at (negative 5, 2). B is located at (−5, 2). If B is reflected across the y-axis, the coordinates will be . If B is reflected across the x-axis, the coordinates will be .
Answer:
the anwser is (5,2) and (-5,-2)
Step-by-step explanation:
The classic 60° triangle has a hypotenuse of length 2, an opposite side of length √3 and an adjacent side of length 1....find the value of Cos(60°)
Answer:
The trigonometric values for cos are C = A/H, which means that to find cos(60), you need to divide the adjacent side by the hypotenuse, which in this case gives you 1/2, so that is the value of cos(60).
I hope this helps!
Step-by-step explanation:
Find the value of x. Then, find the measure of each labelled angle.
x=_
(7x+10)°=_
(15x+16)°=_
Answer:
x = 7deg
Step-by-step explanation:
7x + 10 + 15x + 16 = 180 (angles adjacent to each other in a //polygon are supplementary)
22x = 154
x = 7deg
This is a question on polygons and angles. If you wish to venture further into it/understand this topic better, you may want to follow my Instagram account (learntionary), where I post some of my own notes on certain topics and also some tips that may be useful to you :)